Multiscale materials

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

See Also
In Other Guides
Mean-Field Homogenization
Multiscale Material Modeling

Products Abaqus/Standard

The macroscale properties of the composites predicted by the mean-field homogenization methods are compared to the Finite Element-Representative Volume Element (FE-RVE) predictions. Finite element models of a repeating unit cell use the same constituent properties and microstructure of the composite as the mean-field model. Periodic boundary conditions are applied on the boundary nodes of the unit cell using the following equation:

u i ( x j + p j α ) = u i ( x j ) + u i , k p k α ,
where u i is the nodal displacement, p j α is the α t h vector defining the periodicity of the unit cell, and u i , k is the far-field displacement gradient, which is assumed to be equal to the nominal strain given that the far-field rotation is constrained to be zero. The stress response of the FE-RVE is given by
σ i j = 1 V Ω σ i j V Σ k = 1 , n σ i j k V k Σ k = 1 , n V k .
This stress response can then be used to validate the prediction given by the mean-field homogenization. The FE-RVE can also be used to obtain the stiffness matrix by performing a linear perturbation step with six load cases, with each load case yielding one column of the 6 × 6 matrix. The Coefficient of Thermal Expansions (CTE) can be computed by applying a uniform temperature change across the FE-RVE and measuring the change in the volume-averaged strain.